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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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 Posted: Thu Dec 25, 2008 6:06 pm Post subject: Free Press, Dec 25, 2008 |
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I enjoyed this one (VH).
| Code: | Puzzle: FP122508
+-------+-------+-------+
| 9 . 5 | 1 . . | . . . |
| . . . | . . 6 | 3 . . |
| . . . | . 4 . | 6 1 . |
+-------+-------+-------+
| 5 3 . | . . . | . . 2 |
| . 9 . | 8 2 3 | . 4 . |
| 2 . . | . . . | . 3 6 |
+-------+-------+-------+
| . 4 1 | . 6 . | . . . |
| . . 9 | 7 . . | . . . |
| . . . | . . 4 | 2 . 3 |
+-------+-------+-------+ |
| Quote: | | See if you can solve the BUG+3! |
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Thu Dec 25, 2008 7:42 pm Post subject: |
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| Solution wrote: | At least one of [r2c8]=8, [r7c7]=8, or [r4c7]=9 must be true or else a BUG exists and prevents a unique solution.
[r2c8]=8 => [r9c8]<>8
[r7c7]=8 => [r9c8]<>8
[r4c7]=9 [r4c8]=8 => [r9c8]<>8
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Dec 25, 2008 7:47 pm Post subject: |
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Danny,
Did your solver find that?
If so, I am impressed you could program it!
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Thu Dec 25, 2008 8:04 pm Post subject: |
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| keith wrote: | Danny,
Did your solver find that?
If so, I am impressed you could program it!
Keith |
Keith,
No, my solver didn't do it. One reason is because I don't understand how higher-level eliminations work. I worked it out logically ... and manually! It took several iterations to get a solution that I liked.
So, I guess there's no reason for you to be impressed. 
Regards, Danny
[Addendum:]
Technically speaking, I could program the logic I used into my solver. Nothing I did manually is beyond the current capabilities of my solver. I just never implemented it this way because I didn't know the formal way to implement such a solution. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Dec 25, 2008 9:11 pm Post subject: |
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Danny,
Have you looked at the old Sudoku Programmer's forum? I don't think there would be an algorithm for BUG+n, but there may be other useful stuff.
Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Thu Dec 25, 2008 11:12 pm Post subject: |
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| I didn't take up the challenge because I did it before I read the hidden question. But it did solve with an M-Wing. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Dec 25, 2008 11:16 pm Post subject: |
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Marty,
I think there are also a couple of XY-wings in there. After basics:
| Code: | +-------------+-------------+-------------+
| 9 6 5 | 1 3 78 | 78 2 4 |
| 4 1 2 | 5 78 6 | 3 789 89 |
| 78 78 3 | 2 4 9 | 6 1 5 |
+-------------+-------------+-------------+
| 5 3 4 | 6 79 17 | 189 89 2 |
| 1 9 6 | 8 2 3 | 5 4 7 |
| 2 78 78 | 4 59 15 | 19 3 6 |
+-------------+-------------+-------------+
| 78 4 1 | 3 6 2 | 789 5 89 |
| 3 2 9 | 7 58 58 | 4 6 1 |
| 6 5 78 | 9 1 4 | 2 78 3 |
+-------------+-------------+-------------+ |
Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Thu Dec 25, 2008 11:48 pm Post subject: |
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| Quote: | | I think there are also a couple of XY-wings in there. |
I didn't look for them since I'm presently more enamored of M- and W-Wings. But I did go back for a second try to look at the BUG+3. The only way I know how to do them is via a triple implication chain. One of them led to an invalidity and the remaining DIC solved it. Is there a more elegant way to do these? |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Fri Dec 26, 2008 12:25 am Post subject: |
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| Marty R. wrote: | | But I did go back for a second try to look at the BUG+3. ... Is there a more elegant way to do these? |
I don't think so. But this one is particularly cool because the implication that R9C8 is <7> is so immediate for all three BUG busting candidates.
Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Fri Dec 26, 2008 12:41 am Post subject: |
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| Quote: | | But this one is particularly cool because the implication that R9C8 is <7> is so immediate for all three BUG busting candidates. |
Easy for you to say!! 
But after the fact, it's apparent that I wouldn't have needed my blank grids to solve it. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Fri Dec 26, 2008 3:19 am Post subject: |
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| keith wrote: | Have you looked at the old Sudoku Programmer's forum? I don't think there would be an algorithm for BUG+n, but there may be other useful stuff.
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Keith,
I've found discussions going back to November 2005 in the Players' Forums. Unfortunately, they are more interested in proofs than in making clear what's happening. Also, there are way too many related articles for me to search for a general interpretation. The good news is that Jeff had this habit of updating the head message in threads that he started. Here's an interesting quote:
| Quote: | Theorem:
BUG grids can have either zero or more than one solution, and so are incompatible with a unique solution puzzle. Hence the puzzle solution must come from the non-BUG candidates. (proof)
Corollary 1: If a BUG can be formed out of the list of candidates by LBMs (without solving for any candidate), then the solution to the puzzle must make use of at least one non-BUG candidate. (example, example)
Corollary 2: Any deductions implied by all non-BUG candidates in the grid must be valid. (example)
Corollary 3: Any placement of a candidate which removes all non-BUG candidates is an invalid move. (example, example)
Corollary 4: Any placement of a candidate which forces a grid into a BUG+1 is a valid move. (example)
Corollary 5: Corollaries 1, 2 and 3 can be applied to a BUG-Lite.
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My solution above conforms to Corollary 2. However, once I had the elimination [r9c8]<>8, I then realized that [r9c8]=8 would result in a short forcing net that would eliminate all three non-BUG candidates. This conforms to Corollary 3 ... and would be easy to implement in my old solver. It could also be added to my new solver.
[Addendum: incorrect and deleted!]
Last edited by daj95376 on Fri Dec 26, 2008 3:59 am; edited 2 times in total |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Fri Dec 26, 2008 3:38 am Post subject: |
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I didn't see the obvious implication forcing r9c8=7 but worked on the conditions at r2c9. Both r2c8=8 & r7c7=8 force r2c9=9 but r4c7=9 force r2c9=8. I then easly found two implication chains that showed r2c8<>8 & r4c7<>9, thereby reducing the puzzle to a BUG+1 that set r7c7=8. I guess it is a similar approach, just a rockier road.
Ted |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Fri Dec 26, 2008 3:55 am Post subject: |
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| tlanglet wrote: | I didn't see the obvious implication forcing r9c8=7 but worked on the conditions at r2c9. Both r2c8=8 & r7c7=8 force r2c9=9 but r4c7=9 force r2c9=8. I then easly found two implication chains that showed r2c8<>8 & r4c7<>9, thereby reducing the puzzle to a BUG+1 that set r7c7=8. I guess it is a similar approach, just a rockier road.
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| Code: | [r2c8]=8 => [r2c9]=9
[r7c7]=8 [r7c9]=9 => [r2c9]<>9
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Fri Dec 26, 2008 5:12 am Post subject: |
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[quote="daj95376"] | tlanglet wrote: | I didn't see the obvious implication forcing r9c8=7 but worked on the conditions at r2c9. Both r2c8=8 & r7c7=8 force r2c9=9 but r4c7=9 force r2c9=8. I then easily found two implication chains that showed r2c8<>8 & r4c7<9> [r2c9]=9
[r7c7]=8 [r7c9]=9 => [r2c9]<>9
[/code] |
Thanks Danny for noting the mix-up in my notation. I have to stop working puzzles and submitting posts late in the day .......
Ted |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Fri Dec 26, 2008 10:33 am Post subject: |
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| Code: | *--------------------------------------------------*
| 9 6 5 | 1 3 78 | 78 2 4 |
| 4 1 2 | 5 78 6 | 3 789 89 |
| 78 78 3 | 2 4 9 | 6 1 5 |
|----------------+----------------+----------------|
| 5 3 4 | 6 79 17 | 189 89 2 |
| 1 9 6 | 8 2 3 | 5 4 7 |
| 2 78 78 | 4 59 15 | 19 3 6 |
|----------------+----------------+----------------|
| 78 4 1 | 3 6 2 | 789 5 89 |
| 3 2 9 | 7 58 58 | 4 6 1 |
| 6 5 78 | 9 1 4 | 2 78 3 |
*--------------------------------------------------*
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As it turns out, I was just lucky picking the non-BUG candidates.
Selecting [r2c8]=8 as a non-BUG candidate was trivial.
Selecting [r7c7]=8 as a non-BUG candidate was trivial.
Selecting [r4c7]=9 as a non-BUG candidate was pure luck.
I missed the fact that [r4c7] has <8> three times in [c7]. Fortunately, it didn't matter because [r7c7]=8 took precedence. Whew!!! |
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